Engineers often rely on parametric studies to analyze device performance within different parameter sets and often wonder if it’s possible to go beyond that in order to directly find the best solution. Optimization methods can help by automatically searching the design space efficiently and finding the optimum solution. 

Let’s first define parametric analysis, then explore the differences between these studies and optimization. 

Parametric Analysis

A parameter is defined as a numerical or other measurable factor forming one of a set that defines a system or sets of conditions of its operation. Parameters are elements of a system that are useful or critical to identifying a system or evaluating a system’s performance, status, or condition. As an example, parameters of an equation modeling movement could include the mechanics, masses, dimensions and shapes, and densities and viscosities of fluids within the system. 

A parametric analysis, also known as a sensitivity analysis, is the study of the influence of different geometric or physical parameters or both on the solution of the problem. Parametric analysis is an important tool for design exploration, for instance, to examine the influence of the air gap length on the magnetic force in a contactor.

Altair’s simulation suite offers engineers and designers a range of parametric analysis tools for a variety of use cases. The analysis scenario can be single or multi-parametric including the parameter time, and/or geometric or physical parameters. Altair users can perform parametric studies based on fluids and thermal performance, electromagnetics, motion, vibro-acoustics, structures, and more.

Parametric analysis is based on user-defined solving scenarios, producing “unrefined” solutions. These results need to post-processed in order to find the optimal solution or compromise in an overall design. 

Optimization

Optimization, conversely, is intended to produce an optimal solution or an optimal compromise between competing parameters. Unlike parametric analysis which requires an initial design for examination, optimization offers engineers a blank slate to explore the design space and create optimal designs based on the constraints defined by the user.

Optimization software is based on either deterministic algorithms, which do not consider any uncertainties, or stochastic algorithms, which accommodate model uncertainties using probability distributions. 

Parametric analysis and optimization are closely intertwined, often used as part of a product design and development workflow. A design engineer might use a structural optimization method like topology optimization to develop an initial geometry, then perform target negotiation and trade-off studies using parametric analysis to explore ‘what if’ scenarios. The results of these analyses would then be fed into an optimization algorithm to find the optimal balance of parameters in a system-level study.

In the video below, multidisciplinary optimization is conducted to design and improve performance of a high-performance electric motor. Parameters including electromagnetism, temperature, stress, vibration, and noise and studied independently, then are tied together with an optimization-driven multiphysics approach to resolve conflicting constraints. This solution supports multi-disciplinary teamwork and helps to reduce design times.

Altair SimLab^TM, which offers automated multiphysics workflows for faster analysis and optimization, and Altair HyperWorks^TM, for detailed modeling of complex designs, are two tools that provide robust applications workflows to facilitate optimization studies of parametrized models. 

When solving problems with multiple physics, pre- and post-processing can often be time-consuming, especially for complex assemblies. SimLab makes it easy to set up parametric optimization without extensive domain-specific training, even for part-time analysts. Rather than performing tedious geometry clean-up, highly automated modeling tools in SimLab allow work to be done directly on the geometry, imported, and updated via bi-directional CAD coupling. Users can rapidly explore and evaluate design changes on the fly with live synching to popular parametric CAD systems including CATIA, Pro/E Siemens NX, and SolidWorks.

For high-fidelity modeling of complex geometries, analysts can use HyperWorks to intuitively perform direct modeling for geometry creation and editing, mid-surface extraction, surface and mid-meshing, mesh quality correction, combined with efficient assembly management and process guidance. The HyperWorks Design Explorer is an end-to-end workflow for real time performance prediction and evaluation. 

With Design Explorer, you can:

• Setup your exploration by creating design variables with minimal mouse clicks and responses using model graphics.
• Submit and monitor your exploration.
• Post-process and interpret DOE exploration results using the Results Explorer.
• View the exploration results or load results from individual runs using the exploration summary table.
• Create a dashboard and load results of additional runs for investigation or comparison or plot data related to the exploration runs.
• View plots to analyze results and evaluate design trade-offs without additional solver runs.

Used together in a product design workflow, parametric analysis and optimization can help engineers make quicker and more informed design decisions, ultimately resulting in higher quality products, fewer redesign cycles, and faster time-to-market.